We establish linear lower bounds for the complexity of non-trivial, primitive recursive algorithms from piecewise linear given functions. The main corollary is that logtime algorithms for the greatest common divisor from such givens (such as Stein's) cannot be matched in e ciency by primitive recurs
โฆ LIBER โฆ
Multidimensional greatest common divisor and Lehmer algorithms
โ Scribed by M. S. Waterman
- Publisher
- Springer Netherlands
- Year
- 1977
- Tongue
- English
- Weight
- 659 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0006-3835
No coin nor oath required. For personal study only.
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We investigate a variant of the so-called "binary" algorithm for finding the GCD (greatest common divisor) of two numbers which requires no comparisons. We show that when implemented with carry-save hardware, it can be used to find the modulo B inverse of an n-bit binary integer in a time proportion